Dynamical systems that operate in conjunction with one another and have at least one shared control often benefit from supervision that includes all the control objectives of all the dynamical systems. In some cases, the control objectives of the dynamical systems conflict with each other. In other cases, at least one dynamical system has internally conflicting control objectives. In other cases, the control objectives of the dynamical systems conflict with each other and some dynamical systems have internally conflicting control objectives. For example, a team of unmanned aerial vehicles (UAVs) flying in formation are dynamical systems that share a common control objective to reach a destination at a particular time and with a specific spatial configuration. Additionally, each UAV has unique internal control objectives relating to maintaining their position within the formation. An UAV experiences an internal conflict if an external object is impeding the programmed route and the UAV has to move out of formation to avoid a collision.
Existing hybrid control design methods and multi-model control design methods for such dynamical systems use fixed algorithms to switch from one control law or model to another law or model. The switching logic required to switch laws or models is unwieldy and sometimes leads to undesirable results, particularly if there are a large number of control objectives to manage.
Under conventional hard discrete control laws, a dynamical system may be instructed to switch modes too often in too short a time interval. In some cases, the hard discrete control law switching causes the dynamical system to “chatter” and even become mechanically unstable. For example, an exemplary UAV subjected to conflicting control objectives is instructed to turn left in one instant, stop in the next instant, turn left in the following instant, as so forth with a resultant jerky movement. Additionally, the dynamical system can trigger false alarms when the modes switch too often. Hybrid control design methods and multi-model control design methods do not learn from the dynamical systems in order to evolve the control laws or models over time. Thus, if the hybrid control design methods and/or multi-model control design methods produce system instability for a given system condition, the design methods will again produce the system instability when the given system conditions reoccur.
Other control design methods employ weighted combinations of multiple control objectives using fixed weight prioritization or simplistic closed form expression for each weighting. These control design methods are difficult to develop and often do not adequately capture (or respond to) the prevailing system conditions. These control designs methods do not learn from the dynamical systems to evolve over time.
For the reasons stated above, there is a need to control dynamical systems while avoiding the problems typically associated with hard discrete control law switching of the dynamical systems.